Referee Phil Dowd was asked to review footage of the incident by the Football Association after no action was taken against the player on the field.
Alex appeared to bring his foot down on the Australian's thigh after being tackled but he will not face punishment.
A statement from the Football Association said: "Referee Phil Dowd confirmed to the FA today that he had not seen the incident at the time.
"He was subsequently requested to view footage of the incident. Having done so, Dowd informed the FA that, had he seen the incident, he would not have shown Alex a red card. On this basis, the FA will not be taking any disciplinary action."
The incident was one of a number talking points from the goalless draw. Skipper John Terry was shown a straight red card by Dowd for a wreckless lunge at Leon Osman, while Frank Lampard, Michael Ballack and Ashley Cole were all booked for dissent as the Blues were held to a goalless draw.
It was the first time that Luiz Felipe Scolari's team have failed to win away this season and leaves them a point behind leaders Liverpool at Christmas.
Scolari was so incensed by the performance of Dowd that he refused to speak at the press conference after the game but he knows he now faces a defensive crisis.
Chelsea will not appeal Terry's dismissal and he will now be banned for the next three games, starting with the home match against West Brom on Boxing Day and followed by Sunday's derby with Fulham and the FA Cup third-round clash with Southend.
With Ricardo Carvalho possibly not returning from his hamstring injury until the new year, there is a danger that Branislav Ivanovic will be the only recognised centre-half for Scolari to pick from.
To make matters worse for the Chelsea manager, goalkeeper Petr Cech picked up a thumb injury late on in the match and had difficulty taking his gloves off because of the pain.
Cech hinted that Dowd may have been influenced by the home supporters when he sent off Terry and said: 'It was hard for the ref to see exactly what happened. He had a split second.
'The crowd were behind him and there was a lot of noise. It makes it more difficult for the referee. He made a decision and we have to live with that.
'It's a pity we couldn't win. We could have been top of the league again but it's a good point.
'We have had other chances to go top but we have drawn some games. A lot of teams are dropping points this season and if we had won our games at home we could have been top with a gap.'
